Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization

2025-06-25

AI Summary

Traditional neural cellular automata (NCAs) suffer from deterministic modeling, limiting their ability to capture the inherent stochasticity and heterogeneity of biological systems. To address this, we propose Mixed Neural Cellular Automata (MNCAs), which explicitly model local heterogeneity and stochastic growth dynamics via probabilistic rule assignment, hybrid architecture design, and controllable intrinsic noise. The MNCA framework unifies three key tasks: synthetic tissue growth simulation, morphogenetic robustness analysis, and microscopy image segmentation. Experiments demonstrate that MNCAs maintain superior structural stability under noise perturbations, more accurately reproduce real biological growth patterns, and generate interpretable, spatially adaptive segmentation rules. Our core contribution lies in the deep integration of probabilistic modeling with NCAs—enabling, for the first time, a unified representation of the interplay between stochasticity and determinism during self-organization.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models
• Multiagent Systems: Agent-Based Simulation and Emergent Behavior

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

Neural Cellular Automata (NCAs) are a promising new approach to model self-organizing processes, with potential applications in life science. However, their deterministic nature limits their ability to capture the stochasticity of real-world biological and physical systems. We propose the Mixture of Neural Cellular Automata (MNCA), a novel framework incorporating the idea of mixture models into the NCA paradigm. By combining probabilistic rule assignments with intrinsic noise, MNCAs can model diverse local behaviors and reproduce the stochastic dynamics observed in biological processes. We evaluate the effectiveness of MNCAs in three key domains: (1) synthetic simulations of tissue growth and differentiation, (2) image morphogenesis robustness, and (3) microscopy image segmentation. Results show that MNCAs achieve superior robustness to perturbations, better recapitulate real biological growth patterns, and provide interpretable rule segmentation. These findings position MNCAs as a promising tool for modeling stochastic dynamical systems and studying self-growth processes.

Problem

• Model stochasticity in biological and physical systems
• Enhance robustness in tissue growth simulations
• Improve interpretability in microscopy image segmentation

Innovation

• MNCA combines probabilistic rules with noise
• MNCA models diverse local behaviors effectively
• MNCA enhances robustness in biological simulations